Executive Summary : | The study of dynamical behaviour of a many-body system has been the topic of paramount interest in condensed matter physics. Significant efforts have been made to understand the role of interactions along with other perturbations such as disorder and topology on the behavior of many-body quantum states out of equilibrium. Due to the many-body nature, experimental accessibility as well as a complete theoretical understanding of such systems are difficult. In such as situations, the QWs which are the dynamical evolution of a few particles quantum state provide a bottom-up approach to access some of the key features of interacting systems at few particles level. Due to the experimental advancements in recent years, QWs of single and interacting particles have been observed in various artificial systems making them one of the most versatile testbeds to simulate complex quantum systems. While several studies have been performed based on the QW of identical particles, the field of QW of distinguishable particle is still not well explored which arguably offers more richer physics. The proposed research is based on the QW of interacting distinguishable particles in one dimensional graph where our aim is to focus on some of the most challenging and timely problems those involve the study of dynamical behaviour of interacting quantum systems. In this context we will mainly focus on the topics related to localization in presence of interaction which is well known as the many-body localization. While the topic of MBL deals with a real many-body system, our interest is to obtain possible signatures of MBL through the QWs. In this proposed project, our focus is to address three important questions through the QW of two-component bosons. The first one involves the investigation on the Bloch oscillation and Wannier-Stark localization of two-component bosons. In the second part we will focus on the signatures of many-body localization in the dynamics of two component bosons. In the third problem, we will address the dynamics of defects in the QW of two component bosons. This will enable us to gain insights about the actual many-body system from a few particles perspective which can be experimentally accessed. |